Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation

• Published in: Mathematical modelling and analysis Vol. 25; no. 4; pp. 680 - 701
• Main Authors: Dehestani, Haniye, Ordokhani, Yadollah, Razzaghi, Mohsen
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 13.10.2020
• Subjects: Approximation; Collocation methods; Differential equations; Error analysis; Laguerre functions; Legendre-Laguerre functions; Mathematical analysis; pseudo-operational matrix; variable-order fractional partial integro-differential equations; weakly singular kernel; variable-order fractional partial integro-differential equations; weakly singular kernel; pseudo-operational matrix; Legendre-Laguerre functions
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2020.11692

In this paper, we apply Legendre-Laguerre functions (LLFs) and collocation method to obtain the approximate solution of variable-order time-fractional partial integro-differential equations (VO-TF-PIDEs) with the weakly singular kernel. For this purpose, we derive the pseudo-operational matrices with the use of the transformation matrix. The collocation method and pseudo-operational matrices transfer the problem to a system of algebraic equations. Also, the error analysis of the proposed method is given. We consider several examples to illustrate the proposed method is accurate.